Pi Garden

🎭 The costume trick

One number, three costumes

A half, a 0.5 and a 50% look like three numbers. They are one number.

School files them under three chapters.

Fractions here. Decimals there. Percentages off somewhere else.

½, 0.5 and 50% are one number, in three costumes.

Start here

The whole puzzle, in one flower

This flower is exactly half open. You can write that three ways. All three are true. That is the whole idea: a fraction, a decimal and a percentage are three names for the same amount, never three different amounts.

½ fraction 0.5 decimal 50% percentage

Your turn: drag the bar below. Slide it anywhere between nothing and everything, and watch all three names change together. They never disagree.

nothingthe whole thing
Fraction
1/2
Decimal
0.5
Percentage
50%

Three read-outs, one amount. None of them is more “real” than the others.

Now the trap that catches nearly everyone…

Forty-five beats five. So 0.45 must beat 0.5.

Right?

The trap

0.45 looks bigger than 0.5

Forty-five beats five in ordinary counting, so 0.45 feels like the bigger number. Pick an answer first (no peeking), then watch the disguise come off.

0.5 vs 0.45

One word holds the whole secret.

Per cent is Latin for “out of a hundred”.

The why

Everything counts out of a hundred

A percentage is a fraction with 100 on the bottom, and a decimal’s first two places count those same hundredths. Your turn: tap or drag across this grid to paint squares and watch all three costumes show the same paint.

0 of 100 painted
0
0
0%

Doing the sums

Any score, out of anything, into a percentage

Tests love “out of 50” and “out of 20”. The move is always the same: turn the bottom number into 100, and do to the top whatever you did to the bottom. Change the numbers and see why the tempting answer is wrong.

It goes further than that.

One number owns a costume it will never take off.

Ask a third to wear a decimal… and it runs on forever.

The stranger half

The costume that never quite fits

A half was easy. A quarter, a fifth, a tenth: all of them slip into a neat decimal. But is different. The fraction costume fits it perfectly. The decimal costume never finishes doing up. Your turn: tap “a third” below and watch what the decimal does.

nothingthe whole thing
Fraction
1/3
Decimal
0.333…
Percentage
33⅓%

A third breaks the pattern: the fraction costume fits perfectly, but the decimal never stops. 0.333… forever.

Learn the trick once…

…and three chapters of the book collapse into one.

A half, a 0.5, a 50%: same amount, different outfit. See it once and you have it for good.

One more thing

The costumes are everywhere once you look. A phone battery at 50% is a phone half charged. A shop shouting 25% off is quietly saying a quarter off. Rain at 70% is 0.7 likely. Same amounts, different outfits, every day.

So next time someone swears 0.45 beats 0.5 because forty-five beats five, show them: line the digits up, count the hundredths, and the disguise comes off. This one’s yours now.